Efficient and Strategy-Proof Multi-Unit Object Allocation with Money: (Non)decreasing Marginal Valuations without Qquasi-Linearity
ISER DP No. 1097, August 2020
39 Pages Posted: 25 Sep 2020 Last revised: 26 Feb 2021
Date Written: August 11, 2020
We consider the problem of allocating multiple units of an indivisible object among agents and collecting payments. Each agent can receive multiple units of the object, and his (consumption) bundle is a pair of the units he receives and his payment. An agent's preference over bundles may be non-quasi-linear, which accommodates income effects or soft budget constraints. We show that the generalized Vickrey rule is the only rule satisfying efficiency, strategy-proofness, individual rationality, and no subsidy for losers on rich domains with non-decreasing marginal valuations. We further show that if a domain is minimally rich and includes an arbitrary preference exhibiting both decreasing marginal valuations and a positive income effect, then no rule satisfies the same four properties. Our results suggest that in non-quasi-linear environments, the design of an efficient multi-unit auction mechanism is possible only when agents have non-decreasing marginal valuations.
Keywords: Efficiency, Strategy-Proofness, Non-Quasi-Linear Preferences, Non-Decreasing Marginal Valuations, Decreasing Marginal Valuations, Constant Marginal Valuations, Multi-Unit Auctions
JEL Classification: D44, D47, D71, D82
Suggested Citation: Suggested Citation